I’m afraid you are mistaken. The dollars you borrow from the bank do add to the money supply exactly like any other dollar.
The distinction you make between “real” dollars and the ones the banks create is illusory — you can spend them just the same.
But of course you are absolutely right when you point out the problem with QE.
No doubt we’ll finish up having to deal with the fallout in the next banking crisis, exactly as we did in 2008. The difference between the currency you get as tokens cut from a magazine & the stuff the banks create when someone takes out a loan are that the shop issuing the tokens picks up the tab for one and the taxpayer gets to cover the damage for the other.
Currency is either a way of transferring debt or a way of tracking exchanges round an economy, depending on your point of view. In either case it’s an idea, not a thing — so it can be created & destroyed by belief.